Liquidity and Asset Pricing. Evidence on the role of Investor Holding Period. Randi Næs Norges Bank Bernt Arne Ødegaard Norwegian School of Management BI and Norges Bank UiS, Sep 2007
Holding period This paper: Holding periods of individual investors. Relate to: Asset pricing. Liquidity/Market microstructure.
Asset pricing Determinants of the price of financial assets. Best known example Capital Asset Pricing Model (CAPM). Asset Price P i = f (cov(r i, r m )) r i asset return r m market return Empirically not sufficient Other factors also important for asset prices Firm size Book/Market ratio Stock Market Liquidity
Asset pricing Theoretical Asset Pricing: What is the mechanism for moving asset prices toward equilibrium? Prices align to make investors indifferent between trading / not trading. Does the mechanism for moving prices involve trading? (The microstructure view) Whose trades are then important? Those that buy/sell? Those that do not buy/sell? (The silent majority)
Market Microstructure Explicit modelling of interaction between market participants. Information (Informed/Noise traders) Liquidity (Number of potential traders) Market design (Mechanism for moving prices) Can these effects be viewed as second order? Difference many other markets: Importance of information.
Empirically - Market microstructure affects asset prices Empirical evidence Variables related to microstructure/liquidity important for asset prices US data UK Amihud and Mendelson [1986] Pastor and Stambaugh [2003] Acharya and Pedersen [2005] Korajczyk and Sadka [2007] Datar, Naik, and Radcliffe [1998] Norway (Oslo Børs) Næs, Skjeltorp, and Ødegaard [2007]
Measuring liquidity Theoretically / Empirically: Liquidity - difficult concept. How much must prices move to effectuate an order? Depth of order book Many different liquidity proxies, Bid/Ask Spread (Quoted/Effective) Turnover (Fraction of shares outstanding traded) What is the cost implicit in the market moving and a stock not moving? (r i = a + br m ) Lesmond, Ogden, and Trzcinka [1999] How much volume is needed to move prices? (return) Amihud [2002]...
Liquidity - why does it matter? Liquidity matters for asset pricing. But: Still unclear what aspect of liquidity is important (What moves this from second to first order) Disputed - No single model Why we want to consider holding periods - can they add information?
Amihud and Mendelson [1986] model Often cited link asset pricing - microstructure: The Amihud and Mendelson [1986] model. Investors choose assets depending on the spread. Expect to hold the stocks for a long period Willing to buy high spread stocks. (Higher cost distributed over longer time) Result: Link between Expected return and spread Expected return and turnover (reflecting holding period differences)
Bottom line The whole distribution of how long owners hang on to their stocks likely to be important for asset pricing. However: We have no explicit model we are testing. Analysis in this paper exploratory.
A possible distribution of equity owners Time Day traders Short term Long term
Another possible distribution of equity owners Time Day traders Long term
This paper Source of contribution of this paper: Data on holding periods of All owners in a stock market Over a long time period (10 years).
What do we do? At the level of individual investors. 1) Describe holding period distribution for individual investors. Investigate determinants of holding period. 2) Relate actual holding periods to existing proxies for holding period. At the level of stocks. 3) Look at the link between holding periods and liquidity measures. 4) Ask whether aspects of holding period explain asset prices better than liquidity measures.
Market and Data All firms listed at the Oslo Stock Exchange (OSE) in the period 1992-2003 Data Sources Norwegian Securities Registry (VPS) equity holdings of the complete stock market can distinguish between investor types Oslo Stock Exchange Data Service (OBI) stock prices and accounting data Central Bank of Norway interest rates
Individual Decisions on Holding Period Describe the holding periods of all equity investors in the Norwegian stock market using duration analysis Study what variables might affect holding period decisions Direct test of the spread-holding period relationship in Amihud and Mendelson (1986) Compare with results from existing literature using turnover as a proxy for holding period
Duration Analysis The main tool for analyzing length of time spent in a particular state (economic, social, health) The probability distribution of duration can be specified by a distribution function F (t) = Pr(T < t) which specify that a random variable T is less than some value t Models the decision to terminate a relationship Here, the decision to liquidate the equity holding in a firm
Duration Analysis (2) Several ways to characterize the probability distribution of the termination decision: The survival function; the unconditional probability of surviving beyond a given date S(t) = 1 F (t) = Pr(T t) The hazard function; the probability of termination, conditional of having survived so far λ(t) = f (t), f (t) = df (t)/dt S(t)
The Truncation Problem First Date Investor A Investor B Last Date Investor C 1992 2003 Calendar tim Investor A: correctly estimated Investor B: right truncated Investor C: left truncated
Unconditional Probability Distribution 0.00 0.25 0.50 0.75 1.00 Kaplan Meier survival estimate 0 2 4 6 8 10 analysis time
Conditional Probability Distribution Smoothed hazard estimate.1.2.3.4.5 0 2 4 6 8 10 analysis time
Determinants of the Hazard Function Hazard = f (observables at entry) Variables spread (test of the AM-model) firm characteristics (size, volatility) investor types (financial, foreign,..) size of investment
Determinants of the Hazard Function (2) Variable Hazard ratio pvalue Prob of exit Spread 0.0034 (0.00) Ln(Firm size) 1.0097 (0.00) Ln(Volatility) 1.4317 (0.00) Financial 1.1916 (0.00) Foreign 0.9932 (0.61) Non-financial 1.1157 (0.00) Individual 0.7551 (0.00) Ln(Investment) 0.9829 (0.00) n 1038170 Contribution to the hazard function: coefficient = 1, no contribution coefficient > 1, higher conditional probability coefficient < 1, lower conditional probability
2) Existing proxies for holding period How does the estimates from actual individual owners compare to existing estimates. Atkins and Dyl [1997]: Estimating holding period using turnover. Compare: Average holding period = 1 Turnover NYSE Nasdaq OSE 1975-1989 1983-1991 1992-2003 Average 6.99 4.01 3.33 Median 3.38 2.43 1.96 Considerably longer average holding period than the one year suggested by our duration analysis
Individual Decisions on Holding Period - Summary The average holding period is around 1 year Considerable time variation in the conditional probability of exit Liquidity is important for the holding period decision Estimating holding period from turnover seriously overstates average holding period
Stock Level Analysis Comparing holding period and standard measures of liquidity. Problem: Holding period is an individual owner decision. Liquidity is measured at the level of a stock (aggregates many individuals) Construct a stock level measure of holding period: hpi Holding period index. What are the determinants of the holding period index? How is the holding period index related to other liquidity measures Does the holding period index explain the cross section of stock returns better than alternative liquidity proxies?
Holding Period Index (hpi) - Construction... 12 11 10 9 Owner 1: Owner 2: 8 7 6 5 4 3 2 time t 1 time (month Owner 3: Owner 4: Let w i = weight for owner i 7 hpi = w 1 1 + w 3 12 + w 3 4 12
The Distribution of Holding Period Indices hpi(ew) hpi(vw) 2000 2000 1500 1500 1000 1000 500 500 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Tendency that large owners have longer holding periods than small owners
3) The Link between hpi and Liquidity Correlation Rank correlation hpi(vw) hpi(ew) hpi(vw) hpi(ew) Annual turnover -0.51-0.51-0.48-0.43 Annual relative spread 0.17 0.32 0.15 0.23 Correlations have expected signs Turnover is an imperfect measure of holding period Spread even less linked to holding period.
The Determinants of Holding Period Indices hpi(ew) hpi(vw) Variable coeff pvalue coeff pvalue Constant 0.767 (0.00) 0.548 (0.00) Ln(Firm size) -0.023 (0.00) -0.000 (0.98) Stock volatility 0.579 (0.07) 0.414 (0.14) BM ratio 0.059 (0.00) 0.036 (0.00) Ln(Firm listing age) 0.102 (0.00) 0.038 (0.00) Primary insider fraction -0.122 (0.07) 0.056 (0.36) Largest owner 0.112 (0.00) 0.130 (0.00) n 1118 1118 R 2 0.30 0.11 hpi smaller firm (ew), value firm, older firm, large owner larger Variables related to information have no effects
The Determinants of hpi - Including Liquidity hpi(ew) hpi(ew) hpi(vw) Variable coeff pvalue coeff pvalue Constant 0.719 (0.00) -0.128 (0.20) Ln(Firm size) -0.013 (0.00) 0.021 (0.00) Stock volatility 0.695 (0.01) -2.765 (0.00) BM ratio 0.036 (0.00) 0.063 (0.00) Ln(Firm listing age) 0.097 (0.00) 0.079 (0.00) Primary insider fraction -0.099 (0.09) -0.124 (0.04) Largest owner -0.043 (0.13) -0.012 (0.69) Annual turnover -0.153 (0.00) Annual relative spread 4.776 (0.00) 2.622 (0.00) n 1118 1118 R 2 0.50 0.46 Turnover and spreads affects hpi in expected ways
4) Asset pricing with holding period measures If what is important for asset prices is holding period, then a measure of holding period should do better in explaining asset returns. What is the relationship between holding period indices and returns? Simple portfolio sorting on excess returns Excess return = Portfolio return Risk free return Standard Fama Macbeth asset pricing tests one-factor model three-factor specification
Excess Returns on Sorted Portfolios 10 portfolios sorted on hpi and liquidity measures hpi(ew) hpi(vw) Turnover Spread 1 1.11 1.26 2.04 0.51 2 1.36 1.44 1.20 1.48 3 1.16 1.04 1.37 0.95 4 1.44 0.91 1.41 1.86 5 1.15 1.01 1.94 1.85 6 0.80 1.28 1.86 1.62 7 0.58 1.03 1.61 1.60 8 1.18 0.95 1.78 1.75 9 1.15 0.57 1.39 2.06 10 0.68 1.16 1.63 2.35
Fama Macbeth Analysis Adding hpi/liquidity to an asset pricing model. Method: Fama and MacBeth [1973] Time: t 1 t t + 1... Stock 1 r 1,t X 1,t r 1,t+1 X 1,t+1... 2 r 2,t X 2,t r 2,t+1 X 2,t+1... Elements of b 1. β i + Liqudity/hpi... n r n,t X n,t r n,t+1 X n,t+1... r t = X t ˆb t r t+1 = X t+1ˆb t+1... average 2. β i, Firm Size, B/M + Liqudity/hpi.
Fama Macbeth Analysis Results (1) hpi(ew) hpi(vw) Turnover Spread Constant -0.0016 (0.89) -0.0110 (0.28) 0.0088 (0.04) -0.0063 (0.25) Stock beta -0.0025 (0.45) -0.0018 (0.61) -0.0007 (0.85) 0.0023 (0.56) hpi(ew) 0.0148 (0.27) hpi(vw) 0.0249 (0.02) Turnover -0.0027 (0.29) Rel Spread 0.2559 (0.00) n 114 114 115 115
Fama Macbeth Analysis Results (2) Adding hpi and liquidity measures to a three-factor specification hpi(ew) hpi(vw) Turnover Spread Constant 0.0867 (0.02) 0.0843 (0.01) 0.0861 (0.01) 0.0358 (0.37) Stock beta 0.0027 (0.47) 0.0033 (0.36) 0.0025 (0.44) 0.0039 (0.29) ln(firm size) -0.0045 (0.00) -0.0047 (0.00) -0.0041 (0.00) -0.0021 (0.25) BM ratio 0.0004 (0.93) 0.0007 (0.87) 0.0013 (0.76) 0.0012 (0.79) hpi(ew) 0.0083 (0.55) hpi(vw) 0.0163 (0.13) Turnover -0.0004 (0.88) Rel Spread 0.1630 (0.02) n 114 114 115 115
Summarizing Explored a dataset with detailed data on individual investor holding periods. At the level of individuals Individual owners tend to hold stock for less than a year. Holding period duration dependent. Liquidity affects holding period decision (Amihud and Mendelson [1986] prediction.) Using turnover as a proxy for holding period over-estimates holding period. Stock characteristica Standard liquidity measures / turnover only imperfectly linked to holding period. Liquidity measures based on trading more related to asset prices than holding periods.
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